finite math
posted by Dominic Cigliano on .
Hercules Films is deciding on the price of the video release of its film Bride of the Son of Frankenstein. Marketing estimates that at a price of p dollars, it can sell
q = 240,000 − 15,000p
copies, but each copy costs $4 to make. What price will give the greatest profit?

revenue = price * copies
profit = revenue  cost, so
y = pq  4q
= (24000015000p)(p4)
= 15000(16p)(p4)
= 15000(p^2+20p64)
That's just a parabola with vertex at p=10.